0 & 0.2 & 0.15 \\0.6 & 0 & 0.25 \\0.5 & 0.1 & 0\end{bmatrix} \]ii) **Determine the probability the professor will purchase the current model in 3 years:**To find the probability of being in the same state after three years (P(Si to Si) for i = 1, 2, 3), we can use matrix exponentiation:\[ P^3 = P \times P \times P \]You can calculate this matrix product using a calculator or software. After obtaining \( P^3 \), look at the main diagonal elements, and each element P(i, i) represents the probability of being in state i after 3 years.So, calculate \( P^3 \) and extract the diagonal elements to find the probability of purchasing the current model in 3 years.